korosh23
  • korosh23
Pre-cal 12 Question! Determine the equation in factored form for the polynomial graph. I need the value of 'a' as well. Ex. f(x)= ax^3 +x^2 + x +4 Please wait for the attachment.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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korosh23
  • korosh23
1 Attachment
ganeshie8
  • ganeshie8
Look at the given graph, what are the x intercepts ?
korosh23
  • korosh23
Well, I know that x-int are --> x=-2 multiplicity of 1 x=1 multiplicity of 2 x=3 multiplicity of 1

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ganeshie8
  • ganeshie8
Excellent! next use factor theorem to write an expression for the polynomial
ganeshie8
  • ganeshie8
if \(x=a\) is a zero, then \((x-a)\) is a factor of the polynomial
korosh23
  • korosh23
Yes, until now, this is what I think it is p(x)= (x+2)(x-1)(x-3) we need y-int and value of a
korosh23
  • korosh23
sorry (x-1)^2
ganeshie8
  • ganeshie8
use the information about multiplicity too
ganeshie8
  • ganeshie8
looks good !
ganeshie8
  • ganeshie8
p(x)= a(x+2)(x-1)^2(x-3)
ganeshie8
  • ganeshie8
lets see if we can find the value of \(a\)
korosh23
  • korosh23
ok
ganeshie8
  • ganeshie8
all we're given is a graph so stare at the graph and see if we could use something. .
korosh23
  • korosh23
y-int?
ganeshie8
  • ganeshie8
yeah give it a try
korosh23
  • korosh23
ok wait a moment
ganeshie8
  • ganeshie8
it seems y intercept is -3 ?
korosh23
  • korosh23
yeah I think so so, (0,-3)
ganeshie8
  • ganeshie8
plug that in and find \(a\)
korosh23
  • korosh23
so, this is what I think it is p(x)=a(x-3)(x-1)^2(x+2) -3= a(-3)(-1)^2(+2) -3=-6a so a= -3/-6= 0.5
ganeshie8
  • ganeshie8
looks good !
korosh23
  • korosh23
haha thank you very much for walking me through it. :)
ganeshie8
  • ganeshie8
np:)

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